1. Field of the Invention
The present invention relates generally to a communication system using Low-Density Parity-Check (LDPC) codes, and more particularly, to a channel encoding/decoding apparatus and method for generating LDPC codes of a particular type.
2. Description of the Related Art
In wireless communication systems, link performance significantly decreases due to various noises in channels, a fading phenomenon, and Inter-Symbol Interference (ISI). Therefore, in order to realize high-speed digital communication systems requiring high data throughput and reliability, such as next-generation mobile communication, digital broadcasting, and portable internet, it is necessary to develop a technology for overcoming noises, fading, and ISI. Recently, an intensive study was conducted relating to the use of an error-correcting code in increasing communication reliability by efficiently recovering distorted information.
An LDPC code, which was first introduced by Gallager in the 1960s, has been underutilized due to its complex implementation that could not be resolved by past technology. However, turbo code, which was discovered by Berrou, Glavieux, and Thitimajshima in 1993, shows the performance approximating Shannon's channel limit. Thus, research has been conducted on iterative decoding and graph-based channel encoding along with analyses on performance and characteristic of the turbo code. Due to this research, the LDPC code was restudied in the late 1990s, which proved that LDPC code has performance approximating Shannon's channel limit if it undergoes decoding by applying iterative decoding based on a sum-product algorithm on a Tanner graph (a special case of a factor graph) corresponding to the LDPC code.
The LDPC code is typically represented using a graph representation technique, and many characteristics can be analyzed through the methods based on graph theory, algebra, and probability theory. Generally, a graph model of channel codes is useful for description of codes. By mapping information on encoded bits to vertexes in the graph and mapping relations between the bits to edges in the graph, it is possible to consider a communication network in which the vertexes exchange predetermined messages through the edges. This makes it possible to derive a natural decoding algorithm. For example, a decoding algorithm derived from a trellis, which can be regarded as a kind of graph, can include the well-known Viterbi algorithm and a Bahl, Cocke, Jelinek and Raviv (BCJR) algorithm.
The LDPC code is generally defined as a parity-check matrix, and can be expressed using a bipartite graph, which is referred to as a Tanner graph. In the bipartite graph vertexes constituting the graph are divided into two different types, and the LDPC code is represented by the bipartite graph composed of vertexes, some of which are called variable nodes and the other of which are called check nodes. The variable nodes are mapped one-to-one to the encoded bits.
With reference to FIGS. 1 and 2, a description will be made of a graph representation method for the LDPC code.
FIG. 1 shows an example of a parity-check matrix H1 of the LDPC code composed of 4 rows and 8 columns. Referring to FIG. 1, since the number of columns is 8, an LDPC code generates a length-8 codeword, and the columns are mapped to 8 encoded bits.
FIG. 2 is a diagram illustrating a Tanner graph corresponding to H1 of FIG. 1.
Referring to FIG. 2, the Tanner graph of the LDPC code is composed of 8 variable nodes x1 (202), x2 (204), x3 (206), x4 (208), x5 (210), x6 (212), x7 (214) and x8 (216), and 4 check nodes 218, 220, 222 and 224. An ith column and a jth row in the parity-check matrix H1 of the LDPC code are mapped to a variable node xi and a jth check node, respectively. In addition, a value of 1, i.e., a non-zero value, at the point where an ith column and a jth row in the parity-check matrix H1 of the LDPC code cross each other, indicates that there is an edge between the variable node xi and the jth check node on the Tanner graph as shown in FIG. 2.
In the Tanner graph of the LDPC code, a degree of the variable node and the check node is defined as the number of edges connected to each respective node, and the degree is equal to the number of non-zero entries in a column or row corresponding to the associated node in the parity-check matrix of the LDPC code. For example, in FIG. 2, degrees of the variable nodes x1 (202), x2 (204), x3 (206), x4 (208), x5 (210), x6 (212), x7 (214) and x8 (216) are 4, 3, 3, 3, 2, 2, 2 and 2, respectively, and degrees of check nodes 218, 220, 222 and 224 are 6, 5, 5 and 5, respectively. In addition, the numbers of non-zero entries in the columns of the parity-check matrix H1 of FIG. 1, which correspond to the variable nodes of FIG. 2, are equal to their degrees 4, 3, 3, 3, 2, 2, 2 and 2. The numbers of non-zero entries in the rows of the parity-check matrix H1 of FIG. 1, which correspond to the check nodes of FIG. 2, are equal to their degrees 6, 5, 5 and 5.
In order to express degree distribution for the nodes of the LDPC code, a ratio of the number of degree-i variable nodes to the total number of variable nodes is defined as fi, and a ratio of the number of degree-j check nodes to the total number of check nodes is defined as gi. For instance, for the LDPC code corresponding to FIGS. 1 and 2, f2= 4/8, f3=⅜, f4=⅛, and fi=0 for i≠2, 3, 4; and g5=¾, g6=¼, and gj=0 for j≠5, 6. When a length of the LDPC code, i.e., the number of columns, is defined as N, and the number of rows is defined as N/2, the density of non-zero entries in the entire parity-check matrix having the above degree distribution is computed as Equation (1).
                                                        2              ⁢                                                          ⁢                              f                2                            ⁢              N                        +                          3              ⁢                                                          ⁢                              f                3                            ⁢              N                        +                          4              ⁢                                                          ⁢                              f                4                            ⁢              N                                            N            ·                          N              /              2                                      =                  5.25          N                                    (        1        )            
In Equation (1), as N increases, the density of ‘1’s in the parity-check matrix decreases. Generally, as for the LDPC code, since the code length N is inversely proportional to the density of non-zero entries, the LDPC code with a large N has a very low density of non-zero entries. The wording ‘low-density’ in the name of the LDPC code originates from the above-mentioned relationship.
Next, with reference to FIG. 3, a description will be made of characteristics of a parity-check matrix of a structured LDPC code to be applied in the present invention. FIG. 3 schematically illustrates an LDPC code adopted as the standard technology in Digital Video Broadcasting-Satellite transmission 2nd generation (DVB-S2), which is one of the European digital broadcasting standards.
In FIG. 3, N1 denotes a length of an LDPC codeword, K1 provides a length of an information word, and (N1−K1) provides a parity length. Further, integers M1 and q are determined to satisfy q=(N1−K1)/M1. Preferably, K1/M1 should also be an integer.
Referring to FIG. 3, a structure of a parity part, i.e., K1th column through (N1−1)th column, in the parity-check matrix, has a dual diagonal shape. Therefore, as for degree distribution over columns corresponding to the parity part, all columns have a degree ‘2’, except for the last column having a degree ‘1’.
In the parity-check matrix, a structure of an information part, i.e., 0th column through (K1−1)th column, is made using the following rules.
Rule 1: A total of K1/M1 column groups are generated by grouping K1 columns corresponding to the information word in the parity-check matrix into multiple groups each composed of M1 columns. A method for forming columns belonging to each column group follows Rule 2 below.
Rule 2: Positions of ‘1’s in each 0th column in ith column groups (where i=1, . . . , K1/M1) are first determined. When a degree of a 0th column in each ith column group is denoted by Di, if positions of rows with 1 are assumed to be Ri,0(1), Ri,0(2), . . . , Ri,0(Di), positions Ri,j(k) (k=1, 2, . . . , Di) of rows with 1 are defined as Equation (2), in a jth column (where j=1, 2, . . . , M1−1) in an ith column group.Ri,j(k)=Ri,(j−1)(k)+q mod(N1−K1),  (2)                k=1, 2, . . . , Di, i=1, . . . , K1/M1, j=1, . . . , M1−1        
According to the above rules, it is can be appreciated that degrees of columns belonging to an ith column group (where i=1, . . . , K1/M1) are all equal to Di. For a better understanding of a structure of a DVB-S2 LDPC code that stores information on the parity-check matrix according to the above rules, the following detailed example will be described.
As a detailed example, for N1=30, K1=15, M1=5 and q=3, three sequences for the information on the positions of rows with 1 for 0th columns in 3 column groups can be expressed as follows. Herein, these sequences are called “weight-1 position sequences” for convenience.R1,0(1)=0, R1,0(2)=1, R1,0(3)=2,R2,0(1)=0, R2,0(2)=11, R2,0(3)=13,R3,0(1)=0, R3,0(2)=10, R3,0(3)=14.
Regarding the weight-1 position sequence for 0th columns in each column group, only the corresponding position sequences can be expressed as follows for each column group. For example:
0 1 2
0 11 13
0 10 14.
In other words, the ith weight-1 position sequence in the ith line sequentially represents the information on the positions of rows with 1 in the ith column group.
It is possible to generate an LDPC code having the same concept as that of a DVB-S2 LDPC code of FIG. 4, by forming a parity-check matrix using the information corresponding to the detailed example, and Rule 1 and Rule 2.
It is known that the DVB-S2 LDPC code designed in accordance with Rule 1 and Rule 2 can be efficiently encoded using the structural shape. Respective steps in a process of performing LDPC encoding using the DVB-S2 based parity-check matrix will be described below by way of example.
In the following description, as a detailed example, a DVB-S2 LDPC code with N1=16200, K1=10800, M1=360 and q=15 undergoes an encoding process. For convenience, information bits having a length K1 are represented as (i0, i1, . . . , iKi−1), and parity bits having a length (N1−K1) are expressed as (p0, p1, . . . , pNi−Ki−1).
Step 1: An LDPC encoder initializes parity bits as follows:p0=p1= . . . =pNiKi−1=0
Step 2: The LDPC encoder reads information on a row where 1 is located in a column group from a 0th weight-1 position sequence out of the stored sequences indicating the parity-check matrix.0 2084 1613 1548 1286 1460 3196 4297 2481 3369 3451 4620 2622R1,0(1)=0, R1,0(2)=2048, R1,0(3)=1613, R1,0(4)=1548, R1,0(5)=1286,R1,0(6)=1460, R1,0(7)=3196, R1,0(8)=4297, R1,0(9)=2481, R1,0(10)=3369,R1,0(11)=3451, R1,0(12)=4620, R1,0(13)=2622.
The LDPC encoder updates particular parity bits px in accordance with Equation (3) using the read information and the first information bit i0. Herein, x denotes a value of R1,0(k) for k=1, 2, . . . , 13.p0=p0i0, p2084=p2064i0, p1613=p1613i0,p1548=p1548i0, p1286=p1286i0, p1460=p1460i0,p3196=p3196i0, p4297=p4297i0, p2481=p2481i0,p3369=p3369i0, p3451=p3451i0, p4620=p4620i0,p2622=p2622i0  (3)
In Equation (3), px=pxi0 can also be expressed as px←pxi0, and  denotes binary addition.
Step 3: The LDPC encoder first finds out a value of Equation (4) for the next 359 information bits im (where m=1, 2, . . . , 359) after i0.{x+(m mod M1)×q} mod(N1−K1), M1=360, m=1, 2, . . . , 359  (4)
In Equation (4), x denotes a value of R1,0(k) for k=1, 2, . . . , 13. It should be noted that Equation (4) has the same concept as Equation (2).
Next, the LDPC encoder performs an operation similar to Equation (3) using the value found in Equation (4). That is, the LDPC encoder updates p{x+(m mod M1)×q} mod(N1−K1) for im. For example, for m=1, i.e., for i1, the LDPC encoder updates parity bits p(x+q)mod(N1−K1) as defined in Equation (5).p15=p15i1, p2009=p2009i1, p1628=p1628i1,p1563=p1563i1, p1301=p1301i1, p1475=p1475i1,p3211=p3211i1, p4312=p4312i1, p2496=p2496i1,p3384=p3384i1, p3466=p3466i1, p4635=p4635i1,p2637=p2637i0  (5)
It should be noted that q=15 in Equation (5). The LDPC encoder performs the above process for m=1, 2, . . . , 359, in the same manner as shown above.
Step 4: As in Step 2, the LDPC encoder reads information of the 1st weight-1 position sequence (k=1, 2, . . . , 13) for a 361st information bit i360, and updates a particular px, where x denotes R2,0(k). The LDPC encoder updates p{x+(m mod M1)×q} mod(N1−K1), m=361, 362, . . . , 719 by similarly applying Equation (4) to the next 359 information bits i361, i362, . . . , i719 after i360.
Step 5: The LDPC encoder repeats Steps 2, 3 and 4 for all groups each having 360 information bits.
Step 6: The LDPC encoder finally determines parity bits using Equation (6).pi=pipi−1, i=1, 2, . . . , N1−K1−1  (6)
The parity bits pi of Equation (6) are parity bits that undervent LDPC encoding.
As described above, in DVB-S2, the LDPC encoder performs LDPC encoding through the process of Step 1 through Step 6.
It is well known that performance of the LDPC code is closely related to cycle characteristics of the Tanner graph. In particular, it is well known by experiments that performance degradation may occur when the number of short-length cycles is great in the Tanner graph. Thus, the cycle characteristics on the Tanner graph should be considered in order to design LDPC codes having high performance.
However, no method has been proposed that designs DVB-S2 LDPC codes having good cycle characteristics. For the DVB-S2 LDPC code, an error floor phenomenon is observed at a high Signal to Noise Ratio (SNR) as optimization on cycle characteristics of the Tanner graph is not considered. For these reasons, there is a need for a method capable of efficiently improving cycle characteristics in designing LDPC codes having the DVB-S2 structure.